The city is filled with the carcasses of yesterday’s homes, Once lovely bones picked clean by the copper vultures, Empty frames where glass held back the wind and rain In years now gone and done This was a young couple’s dream for a future together That was a family pausing on the ladder to take…
Author: Clio
Simplify Radicals: Python code
I’m exploring if it’s possible to create a function in GeoGebra that would take an integer as input and create a simplified radical as output. For instance, it would take \(20\) as input and return \(2\sqrt{5}\) as output. I don’t know a way, so if someone does, please tell me. (Edit: There is the SurdText…
Sleepy snowdrift
Sleepy snowdrift Slippery slope Dangling disheartened At the end of my rope Cracking the whip To drive the cart And watch the brickwork Fall apart The age of reason Trumpets change But reasons age And rearrange Somnolent sleeting Succulent slide Dolorous darkened Deliverance died – ptkh 8/18/14
Indeterminate vs. Undefined
Here’s something that seems to confuse many people: \[\frac{1}{0} \text{ is undefined}\\ \frac{0}{0} \text{ is indeterminate}\] If some number, any number at all, divided by zero is undefined, then why isn’t zero divided by zero likewise undefined? And what does “indeterminate” mean anyway? Let’s start with a more concrete question: What is division? Assume we…
The Six Basic Trigonometric Functions
I read an article today on the six basic trigonometric functions, and I thought there was a particularly important insight that I wanted to present in my own words. When I was in school, we learned the six basic trigonometric functions. Since I’ve been teaching, I’ve noticed that only three of these are emphasized: Sine,…
How Many Factors?
A post on G+ Mathematics asks: “How many of the positive divisors of 8400 have four or more positive divisors?” A divisor, or a factor, is an integer which evenly divides another integer; in other words, it is the opposite of a multiple (with the exception of 0). For instance, 8 has the factors {1,…
Modeling in GeoGebra
Introduction In this entry, I’m going to demonstrate the use of GeoGebra to estimate a value for a fairly tricky trigonometry problem, then illustrate how to find the value using trigonometry and an appeal to WolframAlpha. In so doing, I hope to also illustrate the eight basic standards for mathematical practice within Common Core. Here…
Angles and Congruence
Congruence As I discussed in an earlier post, there are two basic definitions of geometric congruence that are presented to students. The first is based on measurement: Definition 1. Two objects are congruent if all of their measurements are the same, and in the same order. That is, two segments are congruent if they’re the…
Programming, Mathematics, and Language
I’ve been struggling for a while now to find a way to frame and articulate the answer to what seems like a simple question: “What is mathematics?” At the same time, I’ve been seeking to layout the similarities and differences between the concepts listed in the title: Computer programming, mathematics, and natural language. Recently, I…
The Golden Ratio and Generalizing Quadratics
A poster on the Google Plus Mathematics community commented that one feature of the Golden Ratio ϕ is that adding one to ϕ yields the same value as squaring ϕ does. That is, \[\phi^2 = \phi + 1\] He was surprised that there would be such a number. While this is indeed an interesting attribute…